Find Minimum in Rotated Sorted List in Python

Uses binary search to find the minimum element in a rotated sorted list in O(log n) time.

Medium Python 3.9+ Aug 9, 2026 Algorithms & data structures 13 views 0 copies

binary-search minimum rotated-array arrays

Python code

14 lines

Python 3.9+

def find_min(nums):
    left, right = 0, len(nums) - 1
    while left < right:
        mid = (left + right) // 2
        if nums[mid] > nums[right]:
            left = mid + 1
        else:
            right = mid
    return nums[left]


if __name__ == "__main__":
    rotated = [4, 5, 6, 7, 0, 1, 2]
    print(f"Minimum: {find_min(rotated)}")

Output

stdout

Minimum: 0

How it works

The algorithm leverages the property of a rotated sorted array: there is exactly one point where the order breaks. By comparing the middle element to the rightmost element, we can determine which half contains the minimum. If the middle is greater than the rightmost, the minimum lies in the right half; otherwise, it is in the left half (including mid). This halves the search space each iteration until left and right converge to the index of the minimum, achieving O(log n) time.

Common mistakes

Using mid = (left + right) // 2 with left < right might cause infinite loops if not updating left correctly
Comparing mid with left instead of right can fail on certain rotations
Forgetting that the list can contain duplicates, which could break the comparison logic
Assuming the list is always rotated; the algorithm should also work for a fully sorted list

Variations

Use recursion instead of iteration to implement binary search
Use Python's built-in min() if O(n) time is acceptable
Handle duplicates by adding linear scans when mid equals right

Real-world use cases

Finding the smallest version number in a circular release history list
Locating the earliest timestamp in a periodically rotated log offset list
Identifying the minimum value in a circularly sorted signal array for anomaly detection

Find Minimum in Rotated Sorted List in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

More from Algorithms & data structures

Tutorials

Quizzes

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

More from Algorithms & data structures

Keep learning

Tutorials

Quizzes